僕は五年ぶりで彼に会える日を楽しみに待っていた。

。

I had been looking forward to the day I could see him again for the first time in five years.

Literal

I [topic-は] five-years-[interval-ぶり] [at-で] him [target-に] can-meet day [object-を] looking-forward-[manner-に] was-waiting.

~ぶり ('for the first time in') marks the interval since the last occurrence. 会える is the potential form of 会う. 楽しみに待つ ('wait with anticipation') — 楽しみ used adverbially with に. ~ていた marks the past ongoing state of waiting. A sentence layered with anticipation.